quan111 2019 1 test2 sol.pdf - TERMS TEST — TEST 2...

TERMS TEST — TEST 2
Trimester 1 - 21/May/2019
QUAN111
MATHEMATICS FOR ECONOMICS
AND FINANCE
Time allowed: SIXTY MINUTES
CLOSED BOOK
Instructions: There are TWENTY multi-choice questions.
Each question is worth ONE mark.
Answer on the multichoice answer sheet provided.
Permitted Materials: Only silent non-programmable calculators or
silent programmable calculators with memories
cleared are permitted in this examination.
Page i of ii

Formulae:
• Linear Function: y = ax + b
• Solving a quadratic function:
f ( x ) = ax
2
+ bx + c = 0 = ⇒ x =
- b ±
√
b 2 - 4 ac
2 a
• Natural exponential function: y = Ae x , where e = 2 . 7182818284 . . .
• Natural logarithmic function: y = ln x
• If A, B are two sets, then
– The union of A and B is denoted by A ∪ B .
– The intersection of A and B is denoted by A ∩ B .
– The difference of A from B is denoted by A \ B .
– If A is a subset of B , then it is denoted by A ⊆ B .
• The inner product of two vectors x and y is denoted by ( x · y )
• The length (or norm ) of vector x is denoted by k x k .
• Solving a quadratic function :
f ( x ) = ax
2
+ bx + c = 0 ⇒ x =
- b ±
√
b
2
- 4 ac
2 a
• Elasticity of demand (for quantity q and price p ): =
dq
dp
p
q
• The first derivative of function f ( x ) with respect to x is denoted by f 0 ( x ).
• Product rule for differentiation: y = f ( x ) g ( x ) ⇒ y 0 = f 0 ( x ) g ( x ) + f ( x ) g 0 ( x )
• Quotient rule for differentiation:
y =
f ( x )
g ( x )
⇒ y
0
=
f 0 ( x ) g ( x ) - f ( x ) g 0 ( x )
( g ( x ))
2
• Chain rule for differentiation: y = f ( g ( x )) ⇒ y
0
= f
0
( g ( x )) g
0
( x )
• Linear approximation of function f ( x ) at x = a :
f ( x ) ≈ f ( a ) + f
0
( a )( x - a )
• Quadratic approximation of function f ( x ) at x = a :
f ( x ) ≈ f ( a ) + f
0
( a )( x - a ) +
1
2
f
00
( a )( x - a )
2
Page ii of ii

QUAN111 TEST 2 21/May/2019